Fractional step algorithm for a model problem in electrochemistry

A new numerical algorithm is introduced to solve the diffusion-migration-convection equations in electrochemistry. The constrained evolution equations are solved by a fractional step approach to decouple the nonlinear interactions of ions. The algorithm composes of a diffusion step, a step for tackling the electroneutrality constraint, and a step for migration to take place. A combination of an implicit scheme, quadratures in one dimension, and an explicit scheme is used in the algorithm for each time increment. Better efficiency is indicated over conventional algorithms. Numerical tests for a uniform flow, two-species system are presented and compared with an exact analytical solution.